What is the 26th Derivative of the Given Function at 0?

[Frillth]

Homework Statement

Given that f(x) = sin(x) for x =/= 0 and f(x) = 1^x for x=0, find the 26th derivative of f at 0. Hint: can you find a power series for f(x)?

The attempt at a solution

I have no idea how to solve this problem. Since 1^x is always 1, the first derivative at 0 is 0, so ALL derivatives must be 0, right? I'm confused as to how a power series even comes into play in this problem.

 

[StatusX]

That's a very strange definition. Note that f(0) is just a number, so all they had to say was f(x)=1 for x=0, the 1^x bit is superfluous. But moreover, the function is not continuous at x=0, so doesn't have any derivatives, let alone 26. Which leads me to ask, are you sure you copied the question correctly?

 

[Frillth]

I just noticed that somebody erased a line in my book! It should have been sin(x)/x for x=/=0 and 1 for x=0. That makes a lot more sense.

 

[arildno]

I advise you to use the hint given!